We now state a very important result regarding well-founded
relations on Polish spaces. We let
\(\mathcal {X}\)  be a Polish space and \(\prec \)  a well-found relation on \(\mathcal {X}\) . We say that \(\prec \)  is analytic if \(R_{\prec } \subseteq \mathcal {X}\times \mathcal {X}\)  is an analytic set. The following theorem, known as Kunen-Martin [1]}, [2]}, bounds the rank function of such a relation.
